It seems that all current transitions could be achieved by having opacity keyframes and additional black or white layers. How about wipe, blur, lens flare or some of the other transitions in applications like Apple Keynote, iMovie or Premiere Pro?

We don't have these effects available as drag-and-drop transitions. This could be submitted as a feature request. There are, however, some workarounds if you don't mind going through the steps:

1.) Wipe: Add a layer mask to the video file, fill the mask with black, unlink the mask, then add Layer Mask Position keyframes to move the layer mask across the video in time (you'll have to have a second clip positioned on a separate track and overlapping in time to get the effect). Add a small feather to the mask in the properties panel to taste (you may want to transform the mask, make sure it's unlinked first, to make it a little larger than the image area if you add feathering).

Diagonal wipes are bit trickier: Follow the same steps above but fill only half the mask with black (on a diagonal, polygon lasso can help with this) and you also need a mask that's larger than the image area so you can pan across (use free transform, make sure the mask is unlinked).

Shape Wipes: I believe this is impossible to do easily, because you would need to transform (scale) the layer mask across time, and this isn't available for layer masks (another feature request if you'd like). Technically you could still pull this off, but you would need to synchronize several different layers/layer masks across time and modify each one so that it forms part of the star shape. That's the only way I can think of currently, if you want something like a star wipe...

2.) Blur: There's a few different ways you could do this. Hardest and most accurate: individually blur each frame by incremental amounts (automate for convenience with an action or script). Different but similar effect: Copy the video, convert the copy to a smart object and place directly below the original on a separate track/video group. Blur the smart object (applies to all frames) and then use opacity keyframes on the original (unblurred) video layer to transition between the two.